Calculate contribution, break-even volume and margin of safety, then test a price reduction without confusing revenue and profit.
A learning club sells a workbook for 25 teaching units. Variable cost is 10 per copy and monthly fixed cost is 900. The planning case is 80 copies. Capacity, tax and mixed products are excluded so the relationship can be inspected clearly.
| Assumption | Value |
|---|---|
| Price per copy | 25 |
| Variable cost per copy | 10 |
| Fixed monthly cost | 900 |
| Planned copies | 80 |
| Alternative price | 22 |
Classify costs by how they behave within the stated range. Fixed does not mean permanent, and variable does not mean uncertain. The model assumes a constant price and unit cost over a relevant range. State these assumptions before calculating so a neat result is not applied outside its conditions.
Classify the case inputs and identify two omitted real-world costs.
Assumption and cost table
Record your result and evidence here or in a separate file.
The 900 monthly amount is not multiplied by copies.
Label each number with its unit and period.
Contribution first covers fixed cost; only the remainder is operating surplus in this simplified model. Break-even quantity is fixed cost divided by unit contribution when contribution is positive. Check the result by rebuilding revenue and total cost at that quantity. A zero or negative contribution requires a different decision.
Calculate contribution and verify break-even with a revenue-cost table.
Break-even calculation
Record your result and evidence here or in a separate file.
Break-even is 60 copies and both revenue and total cost are 1,500 there.
Substitute the answer into the original revenue and cost equations.
Margin of safety compares planned volume with break-even volume. It is not a probability of success. Express it in copies and as a percentage of planned volume, naming that denominator. A plan with a positive margin can still fail if demand, cost or capacity assumptions are wrong.
Calculate surplus and margin of safety at 80 copies.
Volume sensitivity table
Record your result and evidence here or in a separate file.
Surplus is 300, margin is 20 copies or 25% of planned volume.
Use planned volume, not break-even volume, for the stated percentage.
A lower price reduces contribution unless cost changes too. Extra sales may compensate, but the required increase must be calculated. Compare the volume needed to break even and the volume needed to retain the original surplus. Do not assume that a discount automatically creates enough demand.
At price 22, calculate whole-copy break-even and volume needed for a 300 surplus.
Discount decision sheet
Record your result and evidence here or in a separate file.
Break-even requires 75 copies; retaining 300 surplus requires 100 copies.
Round upward only after calculating the target quantity.
A clear recommendation shows which assumptions would make the proposal acceptable. Present a small range of volumes rather than one optimistic estimate. The result is a decision aid for this simplified teaching case. A real pricing decision also needs evidence about customers, competitors, capacity and costs not included here.
Write a 200-word memo comparing prices 25 and 22 at 60, 80 and 100 copies.
Conditional pricing memo
Record your result and evidence here or in a separate file.
The memo identifies the extra 20 copies required to retain the original surplus.
Separate calculated requirements from evidence of achievable demand.
Deliver the cost classification, equations, volume table, discount comparison and conditional memo. Add a variable-cost increase from 10 to 11 and explain its separate effect.
Every break-even quantity is verified against revenue and total cost, with whole-copy rounding made explicit.
| Criterion | Points | Evidence |
|---|---|---|
| Evidence and correctness | 30 | Calculations, source use and results match the supplied case; limitations are honest. |
| Required artifacts | 30 | All five stage outputs and the capstone handoff are present and inspectable. |
| Reasoning and decisions | 20 | Choices, assumptions, alternatives and the case-specific critical condition are explained. |
| Reproducibility | 10 | A reviewer can follow the stated steps and distinguish expected from observed results. |
| Clear communication | 10 | Labels, units, structure and evidence references make the work easy to review. |
Score at least 80/100, supply every required artifact, and satisfy the path-specific critical condition. Rework missing evidence before marking complete.
At price 25, contribution is 15 and break-even is 900 / 15 = 60 copies. At 80 copies, surplus is 300. At price 22, contribution is 12: 75 copies break even and (900 + 300) / 12 = 100 copies retain the 300 surplus.
The model assumes one product and constant unit economics; it is not a forecast or investment recommendation.